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CHAPTER - force
NEWTON'S SECOND LAW OF MOTION
.
(a) Statement
Newton's second law states that "the force acting on a body is directly proportional to the product of
the mass of the body and the acceleration produced in it, the acceleration being in the direction of the
force applied."
(b) Expression (equation for force)
Let a force F acting on a body of mass m produce in it an acceleration a. Then, according to
Newton's second law of motion.
Force α mass x acceleration
i.e.,
F α ma
Or
F=kma
Where k is a constant of proportionality.
Unit force is that force which produces unit acceleration in a body of unit mass,
i.e., if
m = 1 unit and a = 1 unit
Then,
F= 1 unit
Putting, values in equation (1)
We get,
1 = k x 1 x 1, k=I
Equation 1 becomes, F=ma
i.e. Force = mass x acceleration
... (1)
(c) Unit of Force
(i) The S.I. unit of force is newton (N).
One newton is that force which when applied on a body of mass 1 kg produces in it an acceleration of
1 ms-2.
1 newton = 1 kilogram x 1 m s-2
i.e.,
or
1 N = 1 kg x 1 m s-2.
(ii)The C.G.S. unit of force is dyne (dyne).
One dyne is that force which when applied on a body of mass 1 g produces in it an acceleration of
1 cm s-2.
i.e.
or
1 dyne = 1 gram x 1 cm s -2
1 dyn = 1 g x 1 cm s-2.
(iii) Relation between dyne and newton.
1 N = 1 kg x 1 m s-2
= 1000 g x 100 cms-2
= 105 g cm s-2
Or 1 N = 105 dyne.
[Note] Newton and dyne are the absolute units of force.
Gravitational units. Gravitational unit of force is the force which produces acceleration equal to the
acceleration due to gravity in a unit mass.
(i) Kilogram weight (kg. wt.) = g N = 9.8 N
(ii) Gram weight (g. wt.) = g dyne = 980 dyne
Conversion of gravitational units into absolute units
To obtain the value of force, in absolute units, if it is known in gravitational units, we have simply to multiply
by the value of g' in that system. Thus,
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CHAPTER - force
xg wt =x x 980 dyn.
xkgwt =x x 9.8N.
Relation between Force and Momentum
From Newton's second law of motion,
F = ma If a force F applied on a moving body of mass m , changes its velocity from u to u in time t.
or
Force = Rate of change of momentum.
Thus we see that force applied on a body is equal to the rate of change of its momentum and this
change in momentum takes place in direction of force.
IMPULSE OF A FORCE
(a) Introduction
In previous article, we learnt that a moving body has momentum and that an effort (a
force) is needed to stop it. It is our common experience that a smaller force takes more time to
stop the body whereas a bigger force stops the same body in lesser time. This observation
gives concept of a new quantity, force × time, which is named impulse.
(b) Definition
The product of the magnitude of a force applied on a body and the time for which it is
applied, is called impulse of the force. It is represented by the symbol I.
i.e.,
Impulse = Force × Time
Or
I=F. t
The S.I. unit of impulse is Newton-second (N s) and the C.G.S. unit is dyne-second (dyn s).
(c) Impulse and Momentum
From Newton's second law of motion,
This relation is called impulse equation.
(d)Applications of Impulse (or Newton's second law of motion) in Daily Life
(i) Catching the ball by a cricketer. While catching a fast moving cricket ball, the player
moves his hands backward after catching the ball. By moving his hands backward, the cricketer
increases the time. As a result he has to apply a small force on the ball. In reaction, the ball also
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applies lesser force and the hands of the player are not injured.
(ii) Jumping on a heap of sand. If someone jumps from a height on a heap of sand below, his feet
move inside the sand very slowly. His momentum changes slowly requiring a lesser force of
reaction from the sand. Thus man is not injured.
(iii) Springs in vehicles. The vehicles are fitted with springs to reduce the hardness of the shocks.
When vehicles move over an uneven road, they experience impulses exerted by the road. The
springs increase the duration of impulse and hence reduce the force.
(iv) Springs in seats. The seats are also fitted with springs to reduce their hardness. When we sit
on them all of a sudden, the seats are compressed. The compression in creases duration of our
coming to rest on the seat. The reaction force of seats becomes negligible.
BASANT’S physics
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CHAPTER - force
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